Posted by **mr maths** on Friday, January 1, 2010 at 7:45pm.

find the gradient of the tangent to the parabola y=4x-x^2 at (0,0)

hence calculate the size of the angle between the line y=x and this tangent.

(as i cant show you the diagram all that it shows is the line going through (0,0) and having one point of contact)

- maths -
**Reiny**, Friday, January 1, 2010 at 8:05pm
This is a Calculus question.

dy/dx = 4 - 2x

at (0,) dy/dx = 4

so the slope or gradient of the tangent at (0,0) is 4

and the slope of y = x is 1

Did you know that the slope of a line is the same as the tangent of the angle that line makes with the x-axis?

so the line with slope of 4 makes an angle of 75.96º with the x-axis

the line y=x makes and angle of 45º with the x-axis

so the angle between them is (75.96-45)º

= 30.96º

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